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Vector Analysis

Module MA2004

This Module is offered by TUM Department of Mathematics.

This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.

Module version of SS 2020

There are historic module descriptions of this module. A module description is valid until replaced by a newer one.

Whether the module’s courses are offered during a specific semester is listed in the section Courses, Learning and Teaching Methods and Literature below.

available module versions
WS 2020/1SS 2020SS 2012WS 2011/2

Basic Information

MA2004 is a semester module in German language at Bachelor’s level which is offered in winter semester.

This Module is included in the following catalogues within the study programs in physics.

  • Further Modules from Other Disciplines
Total workloadContact hoursCredits (ECTS)
150 h 45 h 5 CP

Content, Learning Outcome and Preconditions


Surfaces and manifolds in Rn. Line and surface integrals. The classical Gauss divergence theorem and Stokes' theorem and generalizations.

Learning Outcome

Having successfully completed this module, the student is able to deal with subsets of n dimensional space which are described by nonlinear functions, and with the corresponding linear approximations as well as with differential and integral formulas on those objects.


MA1001 Analysis 1, MA1002 Analysis 2, MA1101 Linear Algebra and Discrete Structures 1, MA1102 Linear Algebra and Discrete Structures 2

Courses, Learning and Teaching Methods and Literature

Courses and Schedule

Please keep in mind that course announcements are regularly only completed in the semester before.

VO 2 Vector Analysis Warzel, S. Thu, 14:15–15:45, MI HS3
UE 1 Vector Analysis (Exercise Session) Flad, H. Warzel, S. singular or moved dates
and dates in groups

Learning and Teaching Methods

The module is offered as lectures with accompanying practice sessions. In the lectures, the contents will be presented in a talk with demonstrative examples, as well as through discussion with the students. The lectures should animate the students to carry out their own analysis of the themes presented and to independently study the relevant literature. Corresponding to each lecture, practice sessions will be offered, in which exercise sheets and solutions will be available. In this way, students can deepen their understanding of the methods and concepts taught in the lectures and independently check their progress. At the beginning of the module, the practice sessions will be offered under guidance, but during the term the sessions will become more independent, and intensify learning individually as well as in small groups.




K.Jänich, Vektoranalysis, Springer, 2005. English translation: Vector analysis. Springer, 2001.
J.R. Munkres, Analysis on manifolds, Perseus 1991.
M. Spivak, Calculus on Manifolds, Perseus 1965.

Module Exam

Description of exams and course work

Aktueller Hinweis angesichts des eingeschränkten Präsenzbetriebs auf Grund der CoViD19-Pandemie: Die Prüfungsform ändert sich gemäß §13a APSO einmalig auf das Prüfungsformat: einmalige Übungsleistung.
In dieser wird überprüft, inwieweit die Studierenden mit durch nichtlineare Funktionen beschriebenen Teilmengen des n-dimensionalen Raums und den damit verbundenen linearen Approximationen umgehen können sowie Differential- und Integralformeln auf solchen Objekten angemessen anwenden können.

Exam Repetition

The exam may be repeated at the end of the semester.

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